# Temperature in the regulator valve of a cylinder

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1. Sep 20, 2016

### Doppler0y

1. The problem statement, all variables and given/known data

There is a cylinder of oxygen connected to a valve (A) and then to connected to a regulatory valve. The volume of both valves and the pipes between them is Vr and can be disconsidered in regard to the cylinder's volume. The oxygen can be considered a perfect gas with:
$$c_v = 0.653 \frac{kJ}{kg K}$$
$$c_p = 0.915 \frac{kJ}{kg K}$$
Initial cylinder pressure, Pc = 150 bar = 15 * 106Pa
Initial temperature of the conections, Ti = 311K
Initial pressure on the conections, Pi = 1 bar = 105Pa

First question: Considering that the gas from the conections will mix with the oxygen, what is the final temperature in Vr after oppening the valve A?

Second question: Considering that the gases won't mix what will the final temperature be? Considering that both regions won't exchange heat.

2. Relevant equations
In the first question since the process is isochoric
$$T_i \cdot mass \cdot c_p = T_f \cdot mass \cdot c_v$$
in the second question since the process is adiabatic and compressive
$$P \cdot V^γ = constant$$

3. The attempt at a solution

So using the first equation to solve the first question I can divide the mass on both sides and get
$$311 \cdot 0.915 = T_f \cdot 0.653$$
$$T_f = 435.78K$$
But my teacher told me that this value is bit high so maybe I'm using the wrong rationality.

On the second question if someone could give me a suggestion of something to read or a book I would be glad, because I know the heat capacity ratio can be useful in this case I just can't find the right logic to solve it. One thing I know is that the system will be similar to piston inside a motor since the gases will not mix.

2. Sep 26, 2016